Bhavani travels by train from Mumbai to Chennai. List two distinct concepts of mathematics used by her while planning her journey, explaining how they were useful.

Dheeraj says If x is any non-zero number, then x is greater than 1/x is Dheeraj right? Justify your answer.

Which is bigger, 2/3 or 4/5 Give reasons for your answer.

Explain the terms "quotient" and "remainder" with reference to the operation of division. Also suggest an activity to help a child of Class 3 understand these terms.

Give two distinct activities to assess how far a child has understood that a polygon must have at least three sides.

Describe two difficulties children face when dealing with word problems. Your description should include examples.

What is a "hierarchical structure"? Explain this giving one example each from real life, and from mathematics.

Devise two activities for Class 5 children, one each to help them realise that there can be geometrical figures which have

same perimeters but different areas;

same areas but different perimeters.

Give two distinct ways of sharing two chapatis equally among four children.

List the three types of word problems related to division of numbers. Also give an .example of each type.

Give two distinct activities to help children understand the place value representation of decimal fractions.

Give an activity for Class 4 children, designed. to be done in small groups, to help them understand the concept of symmetry.

What is a 'negative number' Write a short story to introduce 'negative numbers' to children of Class 5.

How is the ability of "estimation" important in mathematics Justify your answer with an example related. to spatial understanding.


Use 'mathematical induction' to derive a formula for the sum of the first n odd numbers.

What is the difference between the decimal system and the binary system Convert the decimal number 25 to its binary form.

Give an example of commutativity from the life around you.


Give an example each, with justification, to illustrate the following statements:

The concepts of "instant" and "time-interval" are different.

Using non-standard units of measurement is disadvantageous.

Mention any two errors that a 10-year-old child may make while using a protractor to measure angles.

How will you convince a child that 7/4 is 1 whole and 3/4 more How will you assess the efficacy of your strategy

State two disadvantages of blindly following the mathematics textbook while planning the curriculum.

Give two distinct examples of wrong mathematical generalisations made by
children. For anyone of these, how would you help a child realise why the
generalisation is incorrect?

Azra says that the angle AOB (in the figure below) is the space between OA and OB. Do you agree with Azra Give reasons for your answer.

<img src='./qimages/10423-7c.jpg'>

Explain why 'seriation' is considered a pre-number concept.

List three kinds of errors that children make while studying the concept of 'variable'. For anyone of these, give two distinct activities to help them overcome the misconception.

Explain the process of 'moving from general to particular'. Use an example from 'decimal fractions' in your explanation.

Explain the sequence. How would you apply this sequence while teaching a child to count?

How would you assess whether children in your class have achieved the ability to estimate the product of two integers Give two distinct activities, requiring different ability levels, for this.

10. Which of the following statements are True? Justify your answers.

Pre-operational thinking is characteristic of Class 3 children.

A single mathematical fact can be presented in many ways.

Children should always be working quietly in a mathematics classroom.

Mathematics is best learnt by rote.

'Today is a bright day' is an unambiguous statement.